Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

White light (consisting of wavelengths from $400 n m$ to $700 n m$ ) is normally incident on a grating. Show that, no matter what the value of the grating spacing $d$ , the second order and third order overlap.

It is proved no matter what the value of the grating spacing $d$ , the second order and third order overlap.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

White light has wavelengths between

$λ_{1} = 400 n m$

$λ_{2} = 700 n m$

Step 2: Definition and concept of diffraction from a grating

An optical element with a periodic structure that divides light into a number of beams that move in diverse directions is known as a diffraction grating.

The angular distance of the $m_{t h}$ order diffraction maxima is given by

$d s i n θ = m λ$ …(i)

Here, $λ$ is the wavelength of the incident light and $d$ is the separation between two lines in the grating.

Step 3: Determining the angular distances of second and third order maxima

From equation (i) the angular distance of second order maxima from $λ_{2}$ is

$\begin{array}{l} d sin θ_{2} = 2 x 70 mmm \\ sin θ_{2} = \frac{1400 mm}{d} \end{array}$

From equation (i) the angular distance of third order maxima from $λ_{1}$ is

$\begin{array}{l} d sin θ_{3} = 3 x 400 mm \\ sin θ_{3} = \frac{1200 mm}{d} \end{array}$

Thus

$\sin θ_{2} > \sin θ_{3}$

Hence the angular distance of a part of the second order from white light is greater than the angular distance of a part of the third order. Thus the second and third order overlap.

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Fundamentals Of Physics

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Short Answer

White light (consisting of wavelengths from $400 n m$ to $700 n m$ ) is normally incident on a grating. Show that, no matter what the value of the grating spacing $d$ , the second order and third order overlap.

Step by Step Solution

Step 1: Given data

Step 2: Definition and concept of diffraction from a grating

Step 3: Determining the angular distances of second and third order maxima

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Fundamentals Of Physics

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Short Answer

White light (consisting of wavelengths from 400 nm to 700 nm ) is normally incident on a grating. Show that, no matter what the value of the grating spacing d , the second order and third order overlap.

Step by Step Solution

Step 1: Given data

Step 2: Definition and concept of diffraction from a grating

Step 3: Determining the angular distances of second and third order maxima

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